Question: Solve for $x$ and $y$ using elimination. ${-3x-2y = -22}$ ${-4x+5y = 32}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $2$ ${-15x-10y = -110}$ $-8x+10y = 64$ Add the top and bottom equations together. $-23x = -46$ $\dfrac{-23x}{{-23}} = \dfrac{-46}{{-23}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-3x-2y = -22}\thinspace$ to find $y$ ${-3}{(2)}{ - 2y = -22}$ $-6-2y = -22$ $-6{+6} - 2y = -22{+6}$ $-2y = -16$ $\dfrac{-2y}{{-2}} = \dfrac{-16}{{-2}}$ ${y = 8}$ You can also plug ${x = 2}$ into $\thinspace {-4x+5y = 32}\thinspace$ and get the same answer for $y$ : ${-4}{(2)}{ + 5y = 32}$ ${y = 8}$